podaj trzy pierwsze wyrazy ciągu określanego wzorem a) An = 7n + 1/n b)An = 2n+1/2n-1 c)An= -n^3+2n+5 d)An= 2^n/n^2

a) An = 7n + 1/n a₁=7*1+1/1=8 a₂=7*2+1/2=14 1/2 a₃=7*3+1/3=21 1/3   b) An = (2n+1)/(2n-1) <-- założę się że tak to miało wyglądać a₁=(2*1+1)/(2*1-1)=3/1=3 a₂=(2*2+1)/(2*2-1)=5/3 a₃=(2*3+1)/(2*3-1)=7/5   c) An= -n^3+2n+5 a₁=-1³+2*1+5=-1+2+5=6 a₂=-2³+2*2+5=-8+4+5=1 a₃=-3³+2*3+5=-27+6+5=-16   d) An= (2^n)/(n^2) a₁=(2¹)/(1²)=2/1=2 a₂=(2²)/(2²)=4/4=1 a₃=(2³)/(3²)=8/9      

a) an = 7n + 1/n a1 = 7*1 + 1/1 = 8 a2 =7*2 +1/2 = 14,5 a3 =7*3 + 1/3 = 21 i 1/3 b) an = (2n +1)/(2n -1) a1 = (2*1 +1)/(2*1 -1) = 3/1 = 3 a2 =(2*2 +1)/(2*2 - 1) = 5/3 a3 =(2*3 +1)/(2*3 -1) = 7/5 c) an = - n^3 +2n +5 a1 = - 1³ +2*1 + 5 = -1 +7 = 6 a2 = - 2³ +2*2 + 5 = -8 +4 +5 = 1 a3 = -3³ +2*3 + 5 = -27 +6 +5 = - 16 d) an = 2^n / n² a1 = 2/1² = 2 a2 = 2²/2² = 1 a3 = 2³/3² = 8/9 =====================

[latex]a)a_n=frac{7n+1}{n}\\a_1=frac{7*1+1}{1}=8\\a_2=frac{7*2+1}{2}=7frac{1}{2}\\a_3=frac{7*3+1}{3}=7frac{1}{3}\\b)a_n=frac{2n+1}{2n-1}\\a_1=frac{2*1+1}{2*1-1}=3\\a_2=frac{2*2+1}{2*2-1}=1frac{2}{3}\\c)a_3=frac{2*3+1}{2*3-1}=1frac{2}{5}\\c)a_n=-n^{3}+2n+5\\a_1=-1^{3}+2*1+5=6\\a_2=-2^{3}+2*2+5=1\\a_3=-3^{3}+2*3+5=-16\\d)a_n=frac{2^{n}}{n^{2}}\\a_1=frac{2^{1}}{1^{2}}=2\\a_2=frac{2^{2}}{2^{2}}=1\\a_3=frac{2^{3}}{3^{2}}=frac{8}{9}[/latex]